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Gravitational wave observations have great potential to reveal newinformation about the fundamental nature of gravity, but extracting thatinformation can be difficult. One popular technique is the parametrizedinspiral test of general relativity (a realization of the parametrizedpost-Einsteinian framework), where the gravitational waveform, as calculated inEinstein's theory as a series expansion in the orbital velocity, isparametrically deformed at a given set of orders in velocity. However, mostcurrent approaches usually only analyze the data while considering a single,specific modification at a time. Are then constraints placed with a singlemodification robust to our ignorance of higher post-Newtonian ordercorrections? We show here that for a wide class of theories, specifically thosethat admit a post-Newtonian expansion, single-parameter tests are indeedrobust. In particular, through a series of full Bayesian parameter estimationstudies on several different sets of synthetic data, we show thatsingle-parameter constraints are not degraded but rather are improved by theinclusion of multiple parameters, provided one includes information about themathematical structure of the series. We then exemplify this with a specifictheory of gravity, shift-symmetric scalar Gauss-Bonnet theory, where thewaveform has been calculated to higher post-Newtonian orders than leading. Weshow that the inclusion of these higher order terms strengthenssingle-parameter constraints, instead of weakening them, and that thestrengthening is very mild. This analysis therefore provides strong evidencethat single-parameter post-Einsteinian tests of general relativity are robustto ignorance of high post-Newtonian order terms in the general relativisticdeformations.

Are Parametrized Tests of General Relativity with Gravitational Waves Robust to Unknown Higher Post-Newtonian Order Effects?